// Given a list of lists of possible cage values:
// [[1,2,3], [3,4,5]]
// Recursively generates tuples of combinations from each of the lists as
// follows:
// [1,3]
// [1,4]
// [1,5]
// [2,3]
// [2,4]
// ... etc
// Each of these is checked against the target sum, and pushed into a result
// vector if they match.
// Note: The algorithm assumes that the list of possibles/candidates are
// ordered. This allows it to bail out early if it detects there's no point
// going further.
static void subsetSum(const std::vector<IntList> &possible_lists,
const std::size_t p_size, IntList &tuple,
unsigned tuple_sum, std::vector<IntList> &subsets,
const unsigned target_sum, unsigned list_idx) {
for (unsigned p = list_idx; p < p_size; ++p) {
for (auto &poss : possible_lists[p]) {
// Optimization for small target sums: if the candidate is bigger than
// the target itself then it can't be valid, neither can any candidate
// after it (ordered).
if (target_sum < static_cast<unsigned>(poss)) {
break;
}
// Can't repeat a value inside a cage
if (std::find(tuple.begin(), tuple.end(), poss) != tuple.end()) {
continue;
}
// Pre-calculate the new tuple values to avoid spurious
// insertions/deletions to the vector.
const auto new_tuple_sum = tuple_sum + poss;
const auto new_tuple_size = tuple.size() + 1;
// If we've added too much then we can bail out (ordered).
if (new_tuple_sum > target_sum) {
break;
}
// If there are fewer spots left in the tuple than there are options for
// the sum to reach the target, bail.
// TODO: This could be more sophisticated (can't have more than one 1, so
// it's more like the N-1 sum that it should be greater than.
if ((p_size - new_tuple_size) > (target_sum - new_tuple_sum)) {
break;
}
if (new_tuple_size == p_size) {
// If we've reached our target size then we can stop searching other
// possiblities from this list (ordered).
if (new_tuple_sum == target_sum) {
tuple.push_back(poss);
subsets.push_back(tuple);
tuple.pop_back();
break;
}
// Else, move on to the next candidate in the list.
continue;
}
tuple_sum += poss;
tuple.push_back(poss);
subsetSum(possible_lists, p_size, tuple, tuple_sum, subsets, target_sum,
p + 1);
tuple.pop_back();
tuple_sum -= poss;
}
}
}
TestList()
{
typedef List<char, DebugAllocator<int> > IntList;
IntList a;
a.push_back('1');
a.push_back('2');
a.push_back('3');
LIST_ASSERT(*a.begin() == '1');
LIST_ASSERT(*++a.begin() == '2');
LIST_ASSERT(*++++a.begin() == '3');
LIST_ASSERT(++++++a.begin() == a.end());
IntList b;
b.push_back('a');
b.push_back('b');
b.push_back('c');
LIST_ASSERT(*b.begin() == 'a');
LIST_ASSERT(*++b.begin() == 'b');
LIST_ASSERT(*++++b.begin() == 'c');
LIST_ASSERT(++++++b.begin() == b.end());
// swap full lists
a.swap(b);
LIST_ASSERT(*a.begin() == 'a');
LIST_ASSERT(*++a.begin() == 'b');
LIST_ASSERT(*++++a.begin() == 'c');
LIST_ASSERT(++++++a.begin() == a.end());
LIST_ASSERT(*b.begin() == '1');
LIST_ASSERT(*++b.begin() == '2');
LIST_ASSERT(*++++b.begin() == '3');
LIST_ASSERT(++++++b.begin() == b.end());
// swap to/from empty list
IntList c;
c.swap(b);
LIST_ASSERT(b.empty());
LIST_ASSERT(*c.begin() == '1');
LIST_ASSERT(*++c.begin() == '2');
LIST_ASSERT(*++++c.begin() == '3');
LIST_ASSERT(++++++c.begin() == c.end());
c.swap(b);
LIST_ASSERT(c.empty());
LIST_ASSERT(*b.begin() == '1');
LIST_ASSERT(*++b.begin() == '2');
LIST_ASSERT(*++++b.begin() == '3');
LIST_ASSERT(++++++b.begin() == b.end());
IntList d;
c.swap(d);
LIST_ASSERT(c.empty());
LIST_ASSERT(d.empty());
c.splice(c.end(), d);
LIST_ASSERT(c.empty());
LIST_ASSERT(d.empty());
// splice full with empty
b.splice(b.end(), c);
LIST_ASSERT(c.empty());
LIST_ASSERT(*b.begin() == '1');
LIST_ASSERT(*++b.begin() == '2');
LIST_ASSERT(*++++b.begin() == '3');
LIST_ASSERT(++++++b.begin() == b.end());
// splice empty with full
c.splice(c.end(), b);
LIST_ASSERT(b.empty());
LIST_ASSERT(*c.begin() == '1');
LIST_ASSERT(*++c.begin() == '2');
LIST_ASSERT(*++++c.begin() == '3');
LIST_ASSERT(++++++c.begin() == c.end());
// splice full with full
c.splice(c.end(), a);
LIST_ASSERT(a.empty());
LIST_ASSERT(*c.begin() == '1');
LIST_ASSERT(*++c.begin() == '2');
LIST_ASSERT(*++++c.begin() == '3');
LIST_ASSERT(*++++++c.begin() == 'a');
LIST_ASSERT(*++++++++c.begin() == 'b');
LIST_ASSERT(*++++++++++c.begin() == 'c');
LIST_ASSERT(++++++++++++c.begin() == c.end());
c.pop_back();
LIST_ASSERT(!c.empty());
c.pop_back();
LIST_ASSERT(!c.empty());
c.pop_back();
LIST_ASSERT(!c.empty());
c.pop_back();
LIST_ASSERT(!c.empty());
c.pop_back();
LIST_ASSERT(!c.empty());
c.pop_back();
LIST_ASSERT(c.empty());
}